A Simple General Solution of the Radial Schrodinger Equation for Spherically Symmetric Potentials

Details A Simple General Solution of the Radial Schrodinger Equation for Spherically Symmetric Potentials A Simple General Solution of the Radial Schrodinger Equation for Spherically Symmetric Potentials

2003-05-27

arxiv.org/abs/quant-ph/0305160v1

Physics

Quantum Physics

43 pages, 8 figures, 4 tables

Scientific paper

By using a simple procedure the general solution of the time-independent radial Schrodinger Equation for spherical symmetric potentials was made without making any approximation. The wave functions are always periodic. It appears two diffucilties: one of them is the solution of the equation E= U(r), where E and U(r) are the total an effective potential energies, respectively, and the other is the calculation of the integral of the square root of U(r). If analytical calculations are not possible, one must apply numerical methods. To find the energy wave function of the ground state, there is no need for the calculation of this integral, it is sufficient to find the classical turning points, that is to solve the equation E=U(r).

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